Surely the neighbor won't let the dog out if the yard isn't fenced? The dog could run off and never be seen again. Do many dog owners take that risk?
My thought was that if the dog's yard is no longer fenced, the dog simply wouldn't be out in the yard unsupervised.
My old neighbors were notorious for letting their three awful Pomeranians out the side door and letting them run the neighborhood. They felt that everyone loved them, when the reality was that every.single.person I ever spoke to on our block had murder in their eyes when that topic came up.
That neighborhood was one where everyone had fences on the property lines for the back yards, except that there was a gap on the side of our yard next to the dogs' yard. We quickly put up some inexpensive fencing even though we were renters, to keep our kid in and those animals out.